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Fidelity plateaux from correlated noise in cold-atom quantum simulators

Scott R. Taylor, C. Hooley

Published Nov 14, 2017• 0 citations
OpenAlex

Abstract

We demonstrate that, in a quantum simulation protocol based on the Hubbard model, correlated noise in the Hubbard parameters leads to arbitrarily long plateaux in the state-preparation fidelity as a function of elapsed time. We argue that this correlated-noise scenario is the generic one in the cold-atom context, since all of the Hubbard-model parameters ultimately depend on the same set of lasers. We explain the formation of such a plateau using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height.

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We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced by rotation of the trapping parabolic potential. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases.

•Dec 16, 2015•5 citations
We demonstrate that, in a quantum simulation protocol based on the Hubbard model, correlated noise in the Hubbard parameters leads to arbitrarily long plateaux in the state-preparation fidelity as a function of elapsed time. We argue that this correlated-noise scenario is the generic one in the cold-atom context, since all of the Hubbard-model parameters ultimately depend on the same set of lasers. We explain the formation of such a plateau using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height.
We show that, in an isolated two-level quantum system described by a time-dependent Hamiltonian, correlated noise in the Hamiltonian's parameters can lead to an arbitrarily long plateau in the state-preparation fidelity as a function of elapsed time. We explain the formation of this plateau by using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height. We also briefly discuss the extent to which this phenomenon is expected to be visible in more general quantum systems with N>2N>2N>2 levels.
Laser phase noise is one of the main sources of decoherence in driven Rydberg systems with neutral atoms in tweezer arrays. While the effect of phase noise in the regimes of isolated qubits and few-qubit gate protocols has been studied extensively, there are open questions about the effects of this noise on many-body systems. In many scenarios, the effects of noise cannot simply be described by an increase in the energy or temperature of the system, leading to non-trivial changes in the state and relevant correlations. In this work, we use stochastic sampling to simulate laser phase noise based on experimentally relevant spectral densities. We explore the impact of this noise on adiabatic state preparation in a one-dimensional system, discussing the interplay between heating and interactions during dynamics. We find that for certain adiabatic processes, the noise can be seen to approximately thermalize in terms of its effects on relevant correlation functions.
Hybrid quantum-classical algorithms have been proposed to circumvent noise limitations in quantum computers. Such algorithms delegate only a calculation of the expectation value to the quantum computer. Among them, the Variational Quantum Eigensolver (VQE) has been implemented to study molecules and condensed matter systems on small size quantum computers. Condensed matter systems described by the Hubbard model exhibit a rich phase diagram alongside exotic states of matter. In this manuscript, we try to answer the question: how much of the underlying physics of a 1D Hubbard chain is described by a problem-inspired Variational Hamiltonian Ansatz (VHA) in a broad range of parameter values ? We start by probing how much does the solution increases fidelity with increasing ansatz complexity. Our findings suggest that even low fidelity solutions capture energy and number of doubly occupied sites well, while spin-spin correlations are not well captured even when the solution is of high fidelity. Our powerful simulation platform allows us to incorporate a realistic noise model and show a successful implementation of a noise-mitigation strategy - the Richardson extrapolation.
By means of an adapted mean-field expansion for large fillings n⪢1n⪢1n⪢1, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.
We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced by rotation of the trapping parabolic potential. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases.